Problem: Solve for $x$ and $y$ using elimination. ${-2x-2y = -10}$ ${2x+5y = 16}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $3y = 6$ $\dfrac{3y}{{3}} = \dfrac{6}{{3}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-2x-2y = -10}\thinspace$ to find $x$ ${-2x - 2}{(2)}{= -10}$ $-2x-4 = -10$ $-2x-4{+4} = -10{+4}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 2}$ into $\thinspace {2x+5y = 16}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(2)}{= 16}$ ${x = 3}$